Question

The price, p, for different size orders of custom printed shirts, n, is given in the table.

Can a linear equation be used to model the situation? If it can, what is the slope and the y-intercept of the equation?

Answer 1

linear: slope =10,y-intercept=25

Explanation:

Yes, a linear equation can be used to model the situation because for any two given pints, there is a constant value of 10 for change in (p) over change in (n).

The slope is given by:

`m=(Change\:in\:p)/(Change\:in\:n)`

Using (1,35) and (5,75) from the table, we have:

`m=(75-35)/(5-1)`

`m=(40)/(4)=10`

Therefore the slope is 10.

Using the formula

`y=mx+b`, and the point (1,35) we have:

`35=10(1)+b`

`\implies 35-10=b`

`\implies 25=b`

Therefore the y-intercept is 25.